Monday, Feb. 16, 2004PHYS 1441-004, Spring 2004 Dr. Jaehoon Yu 1 PHYS 1441 – Section 004 Lecture...

Monday, Feb. 16, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu

1

PHYS 1441 – Section 004Lecture #8

Monday, Feb. 16, 2004Dr. Jaehoon Yu

• Chapter four: Newton’s Laws of Motion– Newton’s First Law of Motion– Newton’s Second Law of Motion– Gravitational Force– Newton’s Third Law of Motion– Solving problems using Newton’s Laws

• Uniform circular motion

1st term exam in the class at 1pm, next Monday, Feb. 23!!


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Announcements• Quiz

– Average 53 • Last time: 49• Got considerably better

– Top score: 95• 1st term exam

– Chapter 1 – 5.3 – Mixture of multiple choices and numeric problems

• Will drop the worst of the three term exams– Exams are not comprehensive– Exams constitute 45% of total

• E-mail: – Received 30 verifications Thank you!– I still have 13 of you not registered for e-mail

• Will issue -3 point if not done by next Monday, Feb. 23• - 5 points if not done by Monday, Mar. 1


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Projectile Motion

The only acceleration in this motion. It is a constant!!


4

Maximum Range and Height• What are the conditions that give maximum height and

range of a projectile motion?

g

vh ii

2

sin 22 This formula tells us that the maximum height can be achieved when i=90o!!!

g

vR ii 2sin2

This formula tells us that the maximum range can be achieved when 2i=90o, i.e., i=45o!!!


5

ForceWe’ve been learning kinematics; describing motion without understanding what the cause of the motion was. Now we are going to learn dynamics!!

Can someone tell me what FORCE is?

FORCEs are what cause an object to move

FORCEs are what cause any changes in the velocity of an object!!

The above statement is not entirely correct. Why?Because when an object is moving with a constant velocity no force is exerted on the object!!!

What does this statement mean?

When there is force, there is change of velocity. Forces cause acceleration.

What happens there are several forces being exerted on an object?

Forces are vector quantities, so vector sum of all forces, the NET FORCE, determines the motion of the object.F1 F2 NET FORCE,

F= F1+F2

When net force on an objectis 0, it has constant velocity and is at its equilibrium!!


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More ForceThere are various classes of forces

Contact Forces: Forces exerted by physical contact of objectsExamples of Contact Forces: Baseball hit by a bat, Car collisionsField Forces: Forces exerted without physical contact of objectsExamples of Field Forces: Gravitational Force, Electro-magnetic forceWhat are possible ways to measure strength of Force?A calibrated spring whose length changes linearly with the exerted force.Forces are vector quantities, so addition of multiple forces must be done following the rules of vector additions.


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Newton’s First Law and Inertial FramesAristotle (384-322BC): A natural state of a body is rest. Thus force is required to move an object. To move faster, ones needs higher force.

Galileo’s statement is formulated by Newton into the 1st law of motion (Law of Inertia): In the absence of external forces, an object at rest remains at rest and an object in motion continues in motion with a constant velocity.

A frame of reference that is moving at constant velocity is called an Inertial Frame

What does this statement tell us? • When no force is exerted on an object, the acceleration of the object is 0. • Any isolated object, the object that do not interact with its surroundings, is

either at rest or moving at a constant velocity.• Objects would like to keep its current state of motion, as long as there is no

force that interferes with the motion. This tendency is called the Inertia.

Galileo’s statement on natural states of matter: Any velocity once imparted to a moving body will be rigidly maintained as long as the external causes of retardation are removed!!


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MassMass: A measure of the inertia of a body or quantity of

matter1. Independent of the object’s surroundings: The same no matter where you go.2. Independent of method of measurement: The same no matter how you measure it.

1

2

2

1

a

a

m

mThe same forces applied to two

different masses result in different acceleration depending on the mass.

The heavier an object gets the bigger the inertia!!It is harder to make changes of motion of a heavier object than the lighter ones.

Note that mass and weight of an object are two different quantities!!Weight of an object is the magnitude of gravitational

force exerted on the object. Not an inherent property of an object!!! Weight will change if you measure on the Earth or on the moon.


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Newton’s Second Law of Motion

amFi

i

The acceleration of an object is directly proportional to the net force exerted on it and is inversely proportional to the object’s mass. How do we write the above statement in a mathematical expression?

xi

ix maF Since it’s a vector expression, each component should also satisfy:From the above vector expression, what do you conclude the dimension and unit of force are?

[ ] [ ][ ]Force m a The unit of force in SI is

For ease of use, we define a new derived unit called, a Newton (N)

yi

iy maF zi

iz maF

lbssmkgN4

1/11 2

kg 2/m s


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Acceleration

Example 4.2What constant net force is required to bring a 1500kg car to rest from a speed of 100km/h within a distance of 55m?

This is a one dimensional motion. Which kinetic formula do we use to find acceleration?

What are given?

Thus, the force needed to stop the car is

xF

hkmvxi /100

ifxxixf xxavv 222

What do we need to know to figure out the force? Acceleration!!

Initial speed: sm /28

Displacement: mxxx if 55

Final speed: smvxf /0

if

xixfx xx

vva

2

22

22

/1.7552

/28sm

m

sm

xma

Given the force how far does the car move till it stops?

x

xixfif a

vvxxx

2

22

x

xixf

ma

vvm

2

22 x

xixf

F

vvm

2

22

•Linearly proportional to the mass of the car•Squarely proportional to the speed of the car•Inversely proportional to the force by the brake

2 41500 7.1 / 1.1 10kg m s N

Monday, Feb. 16, 2004 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu

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Acceleration Vector a

F

F

Example for Newton’s 2nd Law of MotionDetermine the magnitude and direction of acceleration of the puck whose mass is 0.30kg and is being pulled by two forces, F1 and F2, as shown in the picture, whose magnitudes of the forces are 8.0 N and 5.0 N, respectively.

xF1

xF

Components of F1

Components of F2

Components of total force F

xa Magnitude and direction of acceleration a

yF1

xF2

yF2

yF

ya a r

a r

NF 0.460cos0.8cos1 o

NF 9.660sin0.8sin1 o

NF 7.420cos0.5cos 22 o

NF 7.120sin0.5sin 22 o

NFF xx 7.87.40.421 xma

NFF yy 2.57.19.621 yma

xF

m 28.7

29 /0.3

m s yF

m 25.2

17 /0.3

m s 22

x ya a 2 229 17

234 /m s1tan y

x

a

a

1 17tan 30

29

o

x ya i a j

229 17 /i j m s


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Gravitational Force and Weight

Since weight depends on the magnitude of gravitational acceleration, g, it varies depending on geographical location.

The attractive force exerted on an object by the Earth

Gravitational Force, Fg

amF G

Weight of an object with mass M is MggMFW G

By measuring the forces one can determine masses. This is why you can measure mass using spring scale.

gm


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Newton’s Third Law (Law of Action and Reaction)If two objects interact, the force, F21, exerted on object 1 by object 2 is equal in magnitude and opposite in direction to the force, F12, exerted on object 1 by object 2. F12

F21

2112 FF

The action force is equal in magnitude to the reaction force but in opposite direction. These two forces always act on different objects. What is the reaction force to the force of a free fall object?

The force exerted by the ground when it completed the motion.

Stationary objects on top of a table has a reaction force (normal force) from table to balance the action force, the gravitational force.


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Example of Newton’s 3rd Law A large man and a small boy stand facing each other on frictionless ice. They put their hands together and push against each other so that they move apart. a) Who moves away with the higher speed and by how much?

2112 FF

b) Who moves farther while their hands are in contact?

M m

F12

F21=-F12

Given in the same time interval, since the boy has higher acceleration and thereby higher speed, he moves farther than the man.

2

2

1tatvx bxbxfb

MaMF 21

2112 FF tatavv MxMxMxiMxf

tatavv bxbxbxibxf

masses theof ratio by the if mMvv Mxfbxf

FFF 2112

bamF 12

21

2b Mxf Mx

Mx v t a t

m

bxx maF 12 012 byy maF

Mxx MaF 21 021 Myy MaF

FFF 2112 Mxbx am

M

m

Fa

2

2ta

m

Mtv

m

MMxMxf

tam

MMx Mxfv

m

M

M

Mx

m

Monday, Feb. 16, 2004PHYS 1441-004, Spring 2004 Dr. Jaehoon Yu 1 PHYS 1441 – Section 004 Lecture...

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Transcript of Monday, Feb. 16, 2004PHYS 1441-004, Spring 2004 Dr. Jaehoon Yu 1 PHYS 1441 – Section 004 Lecture...